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Cells and embryos as flowing shells: analytical and numerical approaches for viscoelastic liquid shells

Presented by: 
Jocelyn Etienne
Friday 11th December 2015 - 15:30 to 16:15
INI Seminar Room 1
Actomyosin networks are known to be much denser at external surfaces of cells and early embryos than in their bulk. They are also known to be the major mechanical element allowing the cell to maintain its shape and governing its dynamics: myosin molecular motors convert biochemical energy into mechanical action, which can resolve in increased tension or deformation depending on boundary conditions [1].

Similarly, during early morphogenesis of embryos, actomyosin forms a surfacic continuum, seamed at cell-cell boundaries by so called adherens junctions, over a thikness of less than a micron at the outer surface of the 50 -micron ellipsoidal embryo. Gene expression is known to lead to successive patternings of myosin density within this actomyosin continuum, which in turn is necessary for the large morphogenetic movements of early embryogenesis to occur. However, while we know that such a myosin patternings are causal, the mechanism by which they govern the correct morphogenetic flows remains unclear. Decyphering it necessitates to resolve the mechanical balance of the embryo with the myosin force-production as a source term.

After presenting the general problem in a closed form suitable for mathematical analysis, I will present three particular cases:
- Single cells in a liquid bridge-like geometry, allowing a partial analytical resolution of the viscoelastic mechanical problem.
- Ventral furrow formation of the Drosophila embryo, for which elasticity approaches are possible at short times.
- The surface flow during germ-band extension of Drosophila, for which we have developped a new surface finite element technique allowing us to solve compressible Stokes-like problems in which velocities are tangential to a curved surface.

[1] J. Étienne, J. Fouchard, D. Mitrossilis, N. Bufi, P. Durand-Smet and A. Asnacios, 2015. Cells as liquid motors: Mechanosensitivity emerges from collective dynamics of actomyosin cortex. Proc. Natl. Acad. Sci. USA 112(9):2740–2745.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons